There are many varieties of "attention", to some extent separate yet working together to produce coherent perception, thought and behaviour. Using data from human behaviour, functional neuroimaging, and single cell recording in the behaving monkey, I consider different levels of attention and their basis in physiological mechanisms of biased competition. Beginning with visual attention, I suggest that processing is competitive in many brain systems that code visual input. Competition is biased towards stimuli that match task requirements, and integrated between systems coding different object properties. The result is flexible, object-based attentional selection. In the second part of the paper, I describe recent experiments on attentional competition within and between sensory modalities. Though competition is often modality-specific, more global levels of interference are also easy to demonstrate. In the third part of the paper, I move to frontoparietal cortex, and to a pattern of similar brain regions recruited by many different cognitive demands. This multiple-demand (MD) pattern, I suggest, reflects neurons with highly flexible response properties, adapting to represent the information and events of many different tasks. Biased competition in MD regions may play a central role in broad attentional capacity limits and attentional focusing. More generally, I suggest that biased competition is characteristic of many different cognitive domains and brain systems. Coherent "attention" develops as different systems converge to work on related cognitive content.